PID Parameter Conversion (Kp/Ti/Td ⇄ Discrete)
Turn ideal-form Kp/Ti/Td into positional and incremental discrete coefficients so you never hand-derive them in code again.
Key points
PID Parameter Conversion (Kp/Ti/Td ⇄ Discrete): Turn ideal-form Kp/Ti/Td into positional and incremental discrete coefficients so you never hand-derive them in code again. Formula: Ki = Kp/Ti ｜ Kd = Kp·Td ｜ discrete Ki = Kp·Ts/Ti. Enter parameters on the DD-CAT IDE online tool page to get results instantly, with a calculation-model diagram that updates with the inputs. The three coefficients of the parallel (ideal) form have different units; the series form (Kp, Ti, Td) is more intuitive — this tool converts between them. Always add integral clamping (anti-windup) and a derivative low-pass in the discrete implementation, or steps saturate the integrator and noise is amplified.
Inputs
Ki = Kp/Ti ｜ Kd = Kp·Td ｜ discrete Ki = Kp·Ts/TiCalculation model (updates with parameters)
| Ki (continuous, 1/s) | 4.0000 | output = Kp·e + Ki·∫e dt |
| Kd (continuous, s) | 0.0400 | |
| Discrete Ki = Kp·Ts/Ti | 0.040000 | |
| Discrete Kd = Kp·Td/Ts | 4.0000 | |
| Incremental coefficient a0 | 6.04000 | Δu = a0·e[k] + a1·e[k−1] + a2·e[k−2] |
| Incremental coefficients a1 / a2 | -10.00000 / 4.00000 | |
| Sample period | 10.000 ms | Ts/Ti = 0.0200 |
Engineering notes
- The three coefficients of the parallel (ideal) form have different units; the series form (Kp, Ti, Td) is more intuitive — this tool converts between them.
- Always add integral clamping (anti-windup) and a derivative low-pass in the discrete implementation, or steps saturate the integrator and noise is amplified.
FAQ
- What is PID Parameter Conversion (Kp/Ti/Td ⇄ Discrete) for?
- Turn ideal-form Kp/Ti/Td into positional and incremental discrete coefficients so you never hand-derive them in code again.
- What is the formula for PID Parameter Conversion (Kp/Ti/Td ⇄ Discrete)?
- Core formula: Ki = Kp/Ti ｜ Kd = Kp·Td ｜ discrete Ki = Kp·Ts/Ti. The tool returns results instantly using this formula and the selected parameters.
- What engineering notes should I keep in mind when using PID Parameter Conversion (Kp/Ti/Td ⇄ Discrete)?
- The three coefficients of the parallel (ideal) form have different units; the series form (Kp, Ti, Td) is more intuitive — this tool converts between them. Always add integral clamping (anti-windup) and a derivative low-pass in the discrete implementation, or steps saturate the integrator and noise is amplified.